Head coach Hodgson was aware of the pressure on Rooney to perform at his best after returning from a two-match ban for his sending off against Montenegro in a qualifying game last October. But, after scoring the winner against Ukraine, Rooney was below par in the quarter-final defeat by Italy when England were beaten 4-2 on penalties after a goalless 120 minutes.
Hodgson said: "I think we put a lot of expectations on Wayne. Wayne certainly tried very hard, but he didn't have his best game. I think he would admit that."
He added: "When he missed the first two games, we were all believing that what we needed to do was to get to the third game and Wayne Rooney will win us the championships.
"That maybe was too much to ask of him."
But Hodgson conceded it was natural for the onus to be on the top players to perform on the biggest stages.
He said: "Do we put too much expectation on Rooney? Well we do, but so do other teams with their players, don't they? I think had (Andrea) Pirlo played poorly, it might have affected the Italians' performance.
"I think in all top international teams, you're looking at one, two, possibly three individuals that everyone recognises as being exceptional world-class talents.
"When you get to the big stage, you're hoping those players perform and show they're world-class talents, like the Maradonas that win Argentina a World Cup with his performance."